Numb3rs botches Simpson’s Paradox

If you watch Numb3rs on CBS, you’ll have noticed a rather bizarre discussion last night of Simpson’s Paradox, which was alleged to say that combing two series of numbers into a single series can change their order (it doesn’t really say that, but that’s beside the point.) The example given was David Justice’s and Derek Jeter’s batting averages in 1995 and 1997. In each year, Justice had a better average than Jeter, but for the total of the two years, Jeter was alleged to have had a better average. It’s not hard to figure out how this could be true, but it wasn’t. The actual numbers for those years are these:

          Justice  H/AB     Jeter    H/AB
          -------           -----
1995       .253   104/411   .250     12/48
1997       .329   163/495   .291   190/654
==========================================
Comb.      .295   267/906   .288   202/702

Justice’s numbers, Jeter’s numbers

If Jeter had hit better in 1997, much closer to Justice’s average, it would have been true because Jeter very few at bats in 1995 and many more at bats in 1997 than Justice. For some bizarre reason, the show used fictitious numbers that didn’t even add up, alleging that Justice hit .321 and .329 for a combined average of .298.

How a show that’s supposed to be so math-oriented can screw up arithmetic so badly would be a a mystery if it weren’t for the fact that mathematicians are notoriously bad at basic arithmetic.

H/T Amnesia, who also got it wrong.

UPDATE: Aha! Reader Brian Thomas explains it all. See comments.